Justin lives in Saint Paul and goes to school in Minneapolis. In the morning, he has $3$ transportation options (bus, cab, or train) to school, and in the evening he has the same $3$ choices for his trip home. If Justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?
Answer: $\text{Probability} = \dfrac{\text{Favorable combinations}}{\text{Total possible combinations}}$ There are $3$ possible choices for each trip, so there are $3\times3=9$ total possible combinations. If Justin chooses randomly, all combinations are equally likely. Each path through the tree represents one possible outcome. The green paths show the $2$ favorable outcomes. $\text{B }$ $\text{C }$ $\text{T }$ $\text{Ride to school}$ $\text{B }$ $\text{C }$ $\text{T }$ $\text{B }$ $\text{C }$ $\text{T }$ $\text{B }$ $\text{C }$ $\text{T }$ $\text{Ride home}$ The probability that Justin will use both the bus and the train is $2$ out of $9$, or $\dfrac29$.